Application and modeling of near-infrared frequency domain photon migration for monitoring pharmaceutical powder blending operations
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Frequency domain photon migration consists of launching an intensitymodulated near-infrared light into the powder medium and measuring the amplitude, mean-intensity, and phase shift of detected intensity modulated light for extracting both the isotropic scattering and absorption coefficients of the powder bed. The dependence of absorption coefficient upon the active pharmaceutical ingredient (API) concentration of powder blend enables FDPM to monitor blending homogeneity. The volume sampled by FDPM in powder blend was investigated through a designed heterogeneity experiments. A model which describes the visitation probability of a local region by migrating photons was developed to theoretically determine the sampled volume of FDPM in terms of signal-to-noise ratio. The applicability of FDPM in monitoring blending homogeneity was directly verified by measuring the API contents in a series of industrial samples, which were retrieved from various locations at various times in an actual pharmaceutical blending process. The FDPM measurement results were consistent with the traditional analysis using high performance liquid chromatography. The homogeneity evolution revealed through FDPM agreed with the well-established first order model of blending. A simulation method was developed which consisted of (i) dynamic simulation for generating the powder structure; (ii) the completely-randommixture model for predicting the spatial distribution of API particles within the powder bed; and (iii) Monte Carlo simulation for tracking photon trajectories within the powder bed. The simulation of photon migration in powder blend revealed that while both the isotropic scattering and absorption coefficients increased with the solid-volume fraction, the ratio of absorption coefficient to the isotropic scattering coefficient is (i) independent of the solid-volume fraction; (ii) linearly dependent upon the API concentration; and (iii) appropriate for monitoring the powder blending homogeneity under simultaneous variations of solid-volume fraction and API content. Finally, a rigorous two-speed diffusion equation for describing photon migration in powders was derived from the two-group radiative transfer equations and the analytical expression of the isotropic scattering coefficient was provided. The theoretical results agreed well with the experimental measurements in resin powder media and resin suspensions.